You are given $893 in one, five, and ten dollar bills. There are 165 bills. There are twice as many five dollar bills as there are ones and tens combined. How many bills of each type are there?

There are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

According to the given situation

You are given $893 in one, five, and ten dollar bills.

Let the number of $1 bills be "x"

Let the number of $5 bills be "y"

Let the number of $10 bills be "z"

Total number of bills = x + y + z  

Also it is given that there are twice as many five dollar bills as there are ones and tens combined

hence we can write the equations in the form of 3 variables

These are three linear equations  with 3 variables that can be solved for x, y and z .

On solving equations (1) , (2),  and (3) we get

So we can conclude that there are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

For more information please refer to the link given below

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Given:

Total number of bills of one, five and ten = 165

Total amount = $893

There are twice as many five dollar bills as there are ones and tens combined.

To find:

Number of bills of each type.

Solution:

Let number of bills of one, five and ten are x, y and z respective.

Total number of bills of is 165.

        ...(i)

Total amount is $893.

        ...(ii)

There are twice as many five dollar bills as there are ones and tens combined.

    ...(iii)

From equation (iii), we get

      ...(iv)

Putting in (i), we get

Putting y=110 in (iv), we get

      ...(v)

Putting y=110 and x=55-z in (ii), we get

Divide both sides by 9.

Putting z=32 in (v), we get

Therefore, the number of one, five and ten bills are 23, 110 and 32 respectively.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!